Modeling strategies for optical lithography have typically applied the continuum approximation to the physics being simulated, meaning the use of continuous mathematics to describe the empirical observations. However, when reduced to a very small scale, the real world is discrete. For example, light energy within a very small volume is comprised of individual photons, and average light intensity is meaningless. Chemicals within a very small volume are comprised of individual molecules, and average chemical concentration is meaningless. Thus, the chemical and photo reactions within such small volumes are discrete and probabilistic—a reactant molecule or a photon might or might not be in a given position within the small volume for a reaction to occur.
As exposure doses decrease and resist dimensions shrink to less than about one hundred nanometers, stochastic resist effects and the effects of critical-dimension scanning electron microscopy upon the resist image become non-negligible.
What is needed, therefore, is a modeling method that overcomes problems such as those described above, at least in part.